This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
This is your last free one today. Let's solve it. Step 1: Identify the given values. Initial velocity of the ball, u = 30 m/s. Acceleration due to gravity, g = 10 m/s^2. Step 2: State the condition for energy. We need to find the height h where the kinetic energy (KE) equals the potential energy (PE). KE = PE (1)/(2)mv^2 = mgh where m is the mass of the ball and v is its velocity at height h. Step 3: Apply the principle of conservation of mechanical energy. The total mechanical energy at the start (ground level) is equal to the total mechanical energy at height h. Initial total energy (E_initial): At h=0, PE_initial = 0. E_initial = KE_initial + PE_initial = (1)/(2)mu^2 + 0 = (1)/(2)mu^2 Total energy at height h (E_at\ h): E_at\ h = KE_at\ h + PE_at\ h Since KE_at\ h = PE_at\ h at this height, we can write: E_at\ h = PE_at\ h + PE_at\ h = 2PE_at\ h = 2mgh Step 4: Equate the initial total energy to the total energy at height h. E_initial = E_at\ h (1)/(2)mu^2 = 2mgh Step 5: Solve for h. Cancel out the mass m from both sides: (1)/(2)u^2 = 2gh h = (u^2)/(4g) Step 6: Substitute the given values and calculate h. h = (30 m/s)^24 × 10 m/s^2 h = 900 m^2/s^240 m/s^2 h = (90)/(4) m h = 22.5 m The height at which its kinetic energy will equal its potential energy is 22.5 m. Comparing this with the given options: A. 45.0 m B. 22.5 m C. 15.0 m D. 30.0 m The correct option is B. The final answer is B. 22.5 m. Last free one today — make it count tomorrow, or type /upgrade for unlimited.